Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 1: Opera mechanica
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CHRISTIANI HUGENII
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evolutione lineæ A E H M, quadrans C L evolutione ſimi-
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lis huic oppoſitæ C O M. </
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diverſitas, quod cum principium quidem curvæ E H M,
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tam in ellipſi quam in hyperbola, ſit punctum E, ſumpta
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A E æquali {1/2} lateris recti; </
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<
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">in hyperbola in infinitum inde
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dicta linea extenditur, at in ellipſi finitur in puncto axis
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minoris M, ſumpta L M æquali {1/2} lateris recti, ſecundum
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quod poſſunt ordinatim applicatæ ad dictum minorem axem.
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</
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<
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">Namque hos terminos eſſe hujus curvæ, facile apparebit or-
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tum ejus conſideranti, quodque in ellipſi eſt ſicut A D ad
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D E, ita L M ad M D.</
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<
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<
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xml:space
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">Horum autem demonſtrationi non immorabimur, ſed ad
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ipſam methodum tradendam pergemus, qua & </
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<
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">hæ curvæ ex
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ſectionibus conicis, & </
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<
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">aliæ innumeræ ex aliis quibuſcun-
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que datis inveniuntur.</
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">PROPOSITIO XI.</
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">DAtâ lineâ curvâ, invenire aliam cujus evolu-
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tione illa deſcribatur; </
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<
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">oſtendere quod ex
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unaquaque curva geometrica, alia curva itidem
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geometrica exiſtat, cui recta linea æqualis dari
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poſſit.</
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<
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">Sit curva quæpiam, vel pars ejus, in partem unam infle-
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Fig. 4. & 5.</
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xa A B F, & </
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tur; </
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<
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">oporteat invenire curvam aliam, ut D E, cujus
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evolutione ipſa A B F deſcribatur.</
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<
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">Ponatur jam inventa; </
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<
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">quoniam tangentes omnes curvæ
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D E, neceſſe eſt occurrere lineæ A B F, ex evolutione de-
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ſcriptæ, ad angulos rectos; </
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<
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ipſi A B F ad rectos angulos inſiſtunt, ut B D, F E, ta-
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cturas evolutam C D E.</
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<
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">Intelligantur autem puncta B, F, inter ſe proxima; </
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quidem à parte A evolutio incipere ponatur, ulteriuſque in-
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de diſtet F quam B, etiam contactus E ulterius quam </
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